Here is a collection of various mathematical notes.

Sheaf cohomology from higher sheaves A note which explains sheaf cohomology of abelian sheaves using the language of higher sheaves. An introduction to higher sheaves is included. Purely from the formalism, we explain why Cech cohomology on an acyclic cover computes cohomology.

Notes on derived stacks Notes on derived stacks written as support for a talk given at an EPFL seminar in autumn 2025. Contains an introduction to infinity-categories, derived rings, cotangent complex, derived (critical) loci.

Mapping spaces of 1-truncated animated rings and transmuted gerbes We explain how to compute mapping spaces between 1-truncated animated rings, and why we get natural gerbes on so called transmuted stacks from Bhatt’s notes prismatic F-Gauges .

Perfectoid rings. A colletion of basic facts about perfectoid rings. Included is a general tilting equivalence, a proof of almost purity for fields and miscellany on completions.

Witt vectors from deformation theory. Finding addition and multiplication of Witt Vectors from deformation theory. Included is a recollection on deformation theory.

Six-functor formalisms. Lecture notes from Marc Hoyois course at the 2023 YTM. Updated from the YTM website version.

Moduli and automorphisms. Quick note to explain the saying that “automorphisms are obstruction to representability of moduli”.

Adjoint functor theorems. Notes on presentable categories and the adjoint functor theorem.